# Topology Seminar

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Wed., Oct. 9, 2019 4:30 p.m.
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Location: Classroom Building (CL) 251
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**Speaker:** Paul Arnaud Songhafouo Tsopméné

**Title:** Simplicial categories and the hammock localization

**Abstract: **Given a category C and a class W of "weak equivalences" in C, one can construct a new category C[W^-1] which as the same objects as C and is obtained from C by formally inverting the maps of W. As shown by Dwyer-Kan, the category C[W^-1] reflects just one aspect of a much richer object, the simplicial localization LC, which is a simplicial category. Because it is difficult to get a hold on the homotopy type of the simplicial set LC(X, Y), for X, Y in C, Dwyer-Kan considered a homotopy variation of LC, the hammock localization L^HC. In this talk I will recall the notion of simplicial category, and explain the construction of the hammock localization. I will also go over some properties of this localization